The Munster game is on February 3, and the Bristol game is on February 9.
It's not the first time the side has played in the northern hemisphere – they played their Super Rugby game against the Sharks at Twickenham as a fundraiser after the 2011 earthquakes in Christchurch.
The chief executive of the Crusaders, Colin Mansbridge, said the side was thrilled to have the chance to play 'some stiff competition away from home'.
"It's also a fantastic chance for our new coaching group to connect, and for our playing group to travel and compete in a new environment."
Munster is the United Rugby Champion and has won the title four times. It beat the Stormers in Cape Town on May 27.
"New Zealand and Australian sides have been working on the World Club Competition for years, so when an opportunity for Super rugby teams to play northern hemisphere counterparts came up, it was just too good to pass up.
"Munster have a history of giving touring sides a pretty hard time, so they present particularly tough competition. There's also the added connection with our new head coach Rob Penney who coached there."
The Bristol side is coached by Pat Lam, the former All Black and Samoan international who was also a Blues Super Rugby coach.
They topped the Premiership table in the 2022-21 season and took out the Challenge Cup in 2019-20.
"It's exciting to play against a club of Bristol's calibre, and one that we already have a relationship with. Razor [outgoing coach Scott Robertson] and Pat Lam have been close for a long time, and Bristol Bears Academy member Andrew Turner made his Crusaders debut this year."
Lam said it would be a special and unique opportunity to have one of the best sides in the world play at their club at Ashton Gate.
"The Crusaders are the reigning Super Rugby champions and we're relishing the opportunity to take on the best club side in the southern hemisphere at what is sure to be a packed-out Ashton Gate."